FinancialBond

FinancialBond works with symbolic parameters and can find closed-form expressions:

Apart can be used to expose the discount factor coefficients on individual payments:

Apart may need to be applied multiple times to fully decompose the expression:

Symbolic solutions to equations involving FinancialBond can be found:

An integer can be used as a payment interval to specify payments occurring only once every several periods:

FinancialBond can be given a term structure of interest rates or a list of future spot rates:

When dates are given along with a rate structure that varies with time, time 0 is assumed to occur at the nearest point before the settlement date that represents an integral number of years from the maturity date. In this case, time 0 occurs on December 31, 2010:

A bond's payment growth function can be any function:

Value a bond under the discount process specified by a force of interest :

FinancialBond can take a functional (growing) coupon together with a force of interest:

A console bond can be valued using Infinity as the maturity date:

Similarly, an equity stock with a growing dividend can be valued using zero face value:

Calculate the duration of the same stock:

FinancialBond takes a nominal yield and assumes a compounding equal to the coupon frequency. However, it may be desirable to use a different compounding frequency. EffectiveInterest can be used to find a rate that gives the correct effective discounting after being compounded at the coupon frequency:

A constant force of interest can be used to create the same continuous compounding:

Expectation can be used to find the expected value of the price of a $1000 par value bond callable at $1100 at some unknown time between years 10 and 15:

Assume the unknown call date will follow a normal distribution centered at year 12.5:

EffectiveInterest can be used to determine the actual discount rates that were used by FinancialBond when a term structure is given:

RSolve can be used to convert recurrence relations into functions of time alone:

The recurrence relation above represents payments growing by a fixed rate, at every payment. Its solution is a function of time alone and is suitable for use in FinancialBond:

Plot bond price against the growth rate of its coupon payment:

A zero coupon bond will pay $1000 at the end of 10 years and is currently selling for $400. Find the implied yield rate compounded semiannually:

Find the price of a 10-year, inflation-adjusted bond with a par value of $1000 and with annual coupons. The initial coupon rate is 7%, and each coupon is 3% greater than the preceding one. The bond's redemption value is $1200:

Find the accrued interest for the bond above, assuming it is purchased three months into its life.

A $100 par value 10-year bond with 8% semiannual coupons is issued on May 1st. Slightly over 2 years later on May 15, the bond sells for $88. Find the yield rate on that date assuming exact calendrical computations:

Price of a semiannual callable bond with a redemption value of $1200, a call date on December 31, 2020, and a settlement date of July 12, 2010:

Days until the next coupon date for a 4% quarterly coupon bond maturing December 31, 2030 and settling September 5, 2013, using the day count convention:

A 20-year semiannual coupon bond has a nominal rate of 8% and a price of $1722.25. The bond can be called at par on any coupon date starting at the end of year 15. Find the par value that will guarantee at least a 6% yield:

Find the call price that will guarantee at least a 7% yield if this same bond had a par value of 1000 and a price of $1300:

Find the maximum yield an investor can hope to achieve if this bond had a call of 1100 and a price of $900:

Duration and convexity for a semiannual bond maturing on December 31, 2030 and settling on November 12, 2010, using the day count convention:

Duration and convexity can be calculated manually using a symbolic yield and the derivative function D:

Calculate the same quantities using FinancialBond properties:

On a coupon date, the value of a FinancialBond object will give the same value as an Annuity object having the same payment frequency and a final payment equal to the par value of the bond:

Although a bond can be defined in terms of an annuity with a final payment, FinancialBond gives a price whereas TimeValue gives a time-valued equivalent for an Annuity. There is no difference when calculating a present value (time = 0), but there are differences when using a time period other than zero:

Plot a bond's actual sensitivity to the yield against its estimated sensitivity given by the duration:

FinancialBond can be used to illustrate the effects of adjusting for accrued interest: